Nathan Coley was listening to Radio 4 when he heard a phrase. The next moment, he was darting up and down his Glasgow flat looking for a pen and paper so he could write it down. The date was 11 September 2011, and the station was broadcasting the memories of people who had been caught up in the 9/11 New York attacks.

Coley, who was shortlisted for the 2007 Turner prize, tells me this a year to the day afterwards, as we sit on the steps of the university library of Pristina, a glorious piece of Soviet architecture. "A woman came on and talked about her memory of sitting in the New York subway about a week after the attacks," says Coley. "She is going back to work – tired, uncertain and not a little frightened. Sitting opposite her is a Sikh man in an orange turban, and her fellow passengers are exhibiting a blatant hatred towards him. He's not returning anyone's gaze, and he's quietly sobbing. Finally, the man gets up at his stop and walks to the door. Standing there is a young black woman holding a baby. The man takes a handful of money and shoves it into the baby's clothing. And at that moment, the woman said she realised that for New York to be the beautiful place we know, it had to find a way to become a place beyond belief."

Across the park – between the new government education offices, the Kosovo Art Gallery, and the half-built, half-ruined Orthodox church raised by Slobodan Milosevic in the 1990s – the phrase that so struck Coley is writ large, picked out in lightbulbs and mounted on a scaffolding frame seven metres tall: "A PLACE BEYOND BELIEF." It is the latest in a series of found-text sculptures by 43-year-old Coley. Placed here, the phrase loses its original context and goes out into the world to find a new life.

The setting is mid-way between reconstruction and ruin: students hurry past between lectures, and newly planted trees grow in spite of the drought. At the same time, the church – a symbol of Serbian oppression to the majority Muslim, ethnic Albanian population – is gradually decaying, weeds filling its cracked brickwork. Tim Judah, a writer and Balkans expert, remembers the church in the immediate aftermath of the 1999 Nato bombing campaign against the Serbians. Inside the shell of the empty building, British troops were encamped "to stop it being destroyed. Of all the things I saw at that time, it was perhaps the most surreal: soldiers watching EastEnders, the Sun on a coffee table – a sort of British living room, in a tent inside this ruin."

Coley's A Place Beyond Belief officially opened earlier this month, in the presence of diplomats and politicians including Martti Ahtisaari, the Finnish ex-president and Nobel laureate who drew up Kosovo's independence plan. These were "the black cars and the grey suits", as Coley puts it, who gathered in the capital to mark another step on Kosovo's road to mature nation-statehood: the end of supervised independence, the system by which, since 2008, Kosovo's political institutions have been overseen.

The sculpture offers a challenge: can this place become a place beyond belief? It hints at an unattainability. "It's somehow the hill beyond the hill you can see," says Coley. This is appropriate in a young country that has its problems: a deeply fragile relationship with Serbia; unanswered questions about the future of its minority Serbian population; corruption and organised crime.

The idea of placing Coley's sculpture here for a month came from Petrit Selimi, Kosovo's deputy minister for foreign affairs. At just 33, he is one of four ministers in Kosovo's government under 35; the president herself is only 36. When, in the early 1990s, Serbia banned ethnic Albanians (about 90% of the Kosovan population) from holding state jobs, and closed Albanian schools and its university, he and his peers were educated by a sort of shadow state, a parallel underground system.

A poster of Ibrahim Rugova, who was the first President of Kosovo. Photograph: Martin Godwin for the Guardian

Selimi was politicised early: he made his debut aged 13, speaking at a youth conference in Vienna. He talks about art with a fluency that is rare in a British politician. "A Place Beyond Belief is multivocal," he says, "it could even be read as antagonistic. At the same time, sited by the church that Milosevic started to build, it stands as a testimony not to religious belief, but the misuse of religious belief. It is also next to the library: between a beacon of hope and a beacon of destruction."

The Kosovo Art Gallery, which organised the installation, is run by Erzen Shkololli, another young man educated in this parallel system. "I was 11 when Milosevic came to power," he says. "I was of the generation who saw the protests and watched Albanian soldiers returning from the war. I've been the witness of so many things that sometimes I feel 66, not 36."

Until a year ago, Shkololli was working in Berlin, a successful artist whose work had been shown internationally. "But if you survive all this, if you get through all these traumas, in the end you want to be here, to contribute here," he says. His role now is to try to nurture a Kosovan art scene: bringing in artists from outside, showing their work alongside that of Balkan artists.

A statue of Clinton in Bill Clinton Boulevard. Photograph: Martin Godwin for the Guardian

Coley's work represents a significant step forward: recent bits of public sculpture in Pristina include a bronze of Bill Clinton who, in the manner of social realist Soviet sculptures, waves benignly in Bill Clinton Boulevard. It's a reminder of how much he (and Tony Blair) are revered in Kosovo, thanks to the 1999 NATO intervention: Selimi says a surprising number of 13-year-old Kosovans are named Tony Blair.

Selimi sees culture as a vital tool for nation-building, a way for Kosovo to present a more mature face to the world. "What do people outside know about Kosovo? They think it's still a war zone, they think of refugees.[Norwegian mass murderer] Anders Breivik mentioned it frequently as a bridge for Islam into Europe. We need to connect to a wider world, and put our story into a greater European and international narrative."This is of crucial importance to a nation whose sovereignty is not recognised by five EU states, not to mention major powers including China and Russia. It is no surprise that Selimi's career pre-politics was in PR (he promoted 50 Cent's first Kosovan gig). "When I was 13, Kosovo was the appendix to nowhere," he says. "We can never again afford to be invisible." He adds, in all seriousness: "For Kosovo to be in the Eurovision Song Contest would be a major victory."

Selemi and Shkololli have a plan: they want to persuade the government to buy a version of A Place Beyond Belief, and to put it permanently on show in the Kosovo parliament building. As a plea to politicians of all stripes not to repeat the terrible mistakes of the past, it's hard to think of a more eloquent message.

• Another version of Nathan Coley's A Place Beyond Belief features in his current exhibition at Haunch of Venison, London W1, until 3 October.